A canonical transformation of the Hamiltonians quadratic in coordinate and momentum operators
1979
An algebraic (matrix) method is presented for canonically transforming the Hamiltonians quadratic in coordinate and momentum operators into the Hamiltonian of non-interacting harmonic oscillators. The method is illustrated by transforming the Hamiltonian of a harmonic oscillator in a constant magnetic field into the Hamiltonian of the two-dimensional, in general anisotropic, harmonic oscillator. The results are found to be in agreement with those obtained previously for the same Hamiltonian using a different technique.
Keywords:
- Anharmonicity
- Hamiltonian (quantum mechanics)
- Quantum electrodynamics
- Harmonic oscillator
- Covariant Hamiltonian field theory
- Mathematical analysis
- Generating function (physics)
- Quantum mechanics
- Creation and annihilation operators
- Canonical transformation
- Mathematics
- Quantum harmonic oscillator
- Classical mechanics
- Physics
- Correction
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